MONEY-WAGE DYNAMICS AND LABOR-MARKET EQUILIBRIUM these two variables together can be supposed to affect acce hence the expected duration of unemployment by anyone contemplating quitting. Second, when a firm finds it has unfilled jobs it will respond with ome combination of additional recruitment expenditures and an at tempted increase of the differential between the wage it pays and the wage paid elsewhere, in order to facilitate recruitment and encourage workers to seek employment at the firm as they learn of the higher differential. The magnitude of the desired differential on this account, for the ith firm, de pends presumably upon the number of vacancies in the firm, Vi, the size of the unemployment pool, U, the number of workers employed elsewhere, Let af denote the ith firms desired wage differential as defined by here w is the average wage paid by all firms and w* is the wage rate which the ith firm wishes to pay. Then the above theory states that Af=j(u, u,U,Vi N-NI, L) ow that j' is homogeneous of degree zero in the last four variables. Then we may write (8) if we neglect the small discrepancy (in the atomistic case) between N/L and (N- N/L. Now if all firms are much alike, we can express the average desired wage differential, denoted A", as a function of both the unemploy- ment rate and the aggregate vacancy rate, U= 2u, (as given in [5]: here I shall suppose 0 m120 Before discussing the postulated shape of the m function, let us take the last step A△*(λ a positive constant,i≡ dw/dt) ew workers -an for a short time! But this tendency will be inhibited con- its know the long- run costs of joining a firm that engages suppose, as an approximation, that new and old workers in a firm receive wage
MONEY-WAGE DYNAMICS AND LABOR-MARKET EQUILIBRIUM (337 these two variables together can be supposed to affect accession rates and hence the expected duration of unemployment by anyone contemplating quitting. Second, when a firm finds it has unfilled jobs it will respond with some combination of additional recruitment expenditures and an attempted increase of the differential between the wage it pays and the wage paid elsewhere, in order to facilitate recruitment and encourage workers to seek employment at the firm as they learn of the higher differential.17 The magnitude of the desired differential on this account, for the ith firm, depends presumably upon the number of vacancies in the firm, V,,the size of the unemployment pool, U, the number of workers employed elsewhere, N - N,, and the size of the labor force, L. Let AT denote the ith firm's desired wage differential as defined by where w is the average wage paid by all firms and w: is the wage rate which the ith firm wishes to pay. Then the above theory states that AT =jl(u, c, U, V,,N -N,,L). Suppose now that j' is homogeneous of degree zero in the last four variables. Then we may write if we neglect the small discrepancy (in the atomistic case) between NIL and (N -N,)/L. Now if all firms are much alike, we can express the average desired wage differential, denoted A*, as a function of both the unemployment rate and the aggregate vacancy rate, c = Cp,(as given in [5]): where I shall suppose Before discussing the postulated shape of the m function, let us take the last step: Pi) -- Ah* (A a positive constant, k = ddwldt). U' l7 Of course the firm will be tempted to pay the higher wage differential only to new workers-and only for a short time! But this tendency will be inhibited considerably if potential recruits know the long-run costs of joining a firm that engages in such sharp practices. I suppose, as an approximation, that new and old workers in a firm receive the same wage
JOURNAL OF POLITICAL ECONOMY This assumes, as mentioned earlier, that each firm expects the wage rate paid by other firms to be constant at least for the duration of the wage negotiated. The rationale of(10), stated loosely, is that the average wage rate will rise(fall) if all firms want to pay a wage higher(lower)than other firms. B It is assumed here that firms in the aggregate adjust their wage only gradually in the direction of the average desired differential; other- wise u and u would be implied to adjust instantaneously to make a' continuously. The gradualness might come from the administrative and psychic cost of changing wage rates that causes wage rates to be changed only intermittently or periodically; if these wage negotiations are stag gered across firms or across workers, then the average wage will move more or less smoothly as indicated In addition, perhaps uncertainty of the firm that the "desired "wage differential, if instituted, would have the desired effect upon turnover costs will induce a cautious, gradual response in the individual firms wage decision As for the postulated shape of the m function, the signs of the derivatives course fundamental to the theory. The excess-demand theory, which is a special case assumes that the second derivatives are zero with m2 =-my= constant>0. My weaker restrictions on the second derivatives in(9b )are inessential they affect only the curvature of the augmented Phillips curve which I shall derive The inequality mu20 meaning that a* decreases with the unemployment rate at a non-increasing rate, vacancy rate constant, is plausible if, as the data suggest (Eagly, 1965), the quit rate is likewise convex with respect to the unemployment rate. The inequality m2220 assumes"rising marginal costs "to the firm of filling vacancies by means other than raising its wage differential. Finally m12 s0 makes sense if it takes a larger increase of the firms wage differen- tial to facilitate the filling of some fraction of a given increment in its vacancies the smaller is the unemployment pool from which workers can conven- iently be drawn. The curve labeled m(u, u)=0 in Figure l gives the com binations of u and u that make 4*=0. Its slope, being -m2/ ml, is necessarily positive, but the size of that slope and the curvature are in determinate and of no qualitative consequence, To the right of this locus and to the left△*<0 In the United States and most other countries, satisfactory vacancy data are still unavailable. I shall couple the above model with a theory of labor turnover or employment dynamics, along lines suggested by Lipsey(1960),in order to derive testableimplicationsofrelations amongeasily observable data The absolute time rate of increase of the aggregate number of persons employed, denoted N= dN/dt, consists of the number of persons hired 18 Stability of the aver exist firms content with /hat counts for the average wage mo is the weighted weighted average differential, say A, which necessarily equals zero)
688 JOURNAL OF POLITICAL ECONOMY This assumes, as mentioned earlier, that each firm expects the wage rate paid by other firms to be constant at least for the duration of the wage negotiated. The rationale of (lo), stated loosely, is that the average wage rate will rise (fall) if all firms want to pay a wage higher (lower) than other firms.18 It is assumed here that firms in the aggregate adjust their wage only gradually in the direction of the average desired differential; otherwise z. and u would be implied to adjust instantaneously to make A* = 0 continuously. The gradualness might come from the administrative and psychic cost of changing wage rates that causes wage rates to be changed only intermittently or periodically; if these wage negotiations are staggered across firms or across workers, then the average wage will move more or less smoothly as indicated. In addition, perhaps uncertainty of the firm that the "desired" wage differential, if instituted, would have the desired effect upon turnover costs will induce a cautious, gradual response in the individual firm's wage decision. As for the postulated shape of the m function, the signs of the derivatives in (9a) are of course fundamental to the theory. The excess-demand theory, which is a special case, assumes that the second derivatives are zero with m2 = -ml = constant > 0. My weaker restrictions on the second derivatives in (9b) are inessential; they affect only the curvature of the augmented Phillips curve which I shall derive. The inequality m,, 2 0, meaning that A* decreases with the unemployment rate at a non-increasing rate, vacancy rate constant, is plausible if, as the data suggest (Eagly, 1965), the quit rate is likewise convex with respect to the unemployment rate. The inequality m2, L 0 assumes "rising marginal costs" to the firm of filling vacancies by means other than raising its wage differential. Finally m12 5 0 makes sense if it takes a larger increase of the firm's wage differential to facilitate the filling of some fraction of a given increment in itsvacancies the smaller is the unemployment pool from which workers can conveniently be drawn. The curve labeled m(u, z.) = 0 in Figure 1 gives the combinations of u and c that make A* = 0. Its slope, being -m2/ml, is necessarily positive, but the size of that slope and the curvature are indeterminate and of no qualitative consequence. To the right of this locus A* > 0, and to the left A* < 0. In the United States and most other countries, satisfactory vacancy data are still unavailable. I shall couple the above model with a theory of labor turnover or employment dynamics, along lines suggested by Lipsey (l960), in ordertoderive testableimplicationsofrelations among easily observable data. The absolute time rate of increase of the aggregate number of persons employed, denoted N = dN/dt, consists of the number of persons hired l8 Stability of the average wage is consistent with some positive differentials if there exist firms content with negative ones. What counts for the average wage movement is the weighted average desired differential, A* (in relation to the ex post, actual, weighted average differential, say A, which necessarily equals zero)
MONEY-WAGE DYNAMICS AND LABOR-MARKET EQUILIBRIUM △"<o (,v)=z=(1-可) z(u, v)= z(u, v)=z= const.>Ov FIG. 1.-Relations between vacancy and unemployment rates per unit time from the unemployment pool, denoted R, less the departures (due to death and retirement) per unit time of employed persons from the labor force, denoted D, and the quitting of employees to join the un employed in search of new jobs, denoted 2. This accountin voluntary terminations and layoffs, which I shall not treat, and it assumes that entrants to the labor force first enter the unemployment pool before being hired. Of course, the accessions and separations of employed ersons who transfer directly from one firm to another cancel out and do not add to n. that is N=R-D-Q shall make the variables on the right-hand side of (11)depend in the ggregate only upon unemployment (or employment), vacancies, and the labor supply. While the hire and quit rates of the individual firm depend upon its actual wage differential, the weighted average actual differential across all firms must be constant(being equal to zero), so one expects vage differentials to wash out in the aggregates I shall suppose that D is proportional to employment, 8 being the factor of proportionality. (This neglects any effect of a real wage change on people at the retirement margin. To eliminate scale effects (rightly or not), I shall take new hires and quits to be homogeneous of degree one Perhaps the dispersion of the wage differentials has some effect upon R and Q
MONEY-WAGE DYNAMICS AND LABOR-MARKET EQUILIBRIUM FIG.1.-Relations between vacancy and unemployment rates per unit time from the unemployment pool, denoted R, less the departures (due to death and retirement) per unit time of employed persons from the labor force, denoted D, and the quitting of employees to join the unemployed in search of new jobs, denoted Q. This accounting ignores involuntary terminations and layoffs, which I shall not treat, and it assumes that entrants to the labor force first enter the unemployment pool before being hired. Of course, the accessions and separations of employed persons who transfer directly from one firm to another cancel out and do not add to N. That is, 1 shall make the variables on the right-hand side of (1 1) depend in the aggregate only upon unemployment (or employment), vacancies, and the labor supply. While the hire and quit rates of the individual firm depend upon its actual wage differential, the weighted average actual differential across all firms must be constant (being equal to zero), so one expects wage differentials to wash out in the aggregates.lg I shall suppose that D is proportional to employment, 6 being the factor of proportionality. (This neglects any effect of a real wage change on people at the retirement margin.) To eliminate scale effects (rightly or not), I shall take new hires and quits to be homogeneous of degree one in l9 Perhaps the dispersion of the wage differentials has some effect upon R and Q